The question of the formation of alpha-clusters in nuclei is an important issue for nuclear physics, as illustrated by the famous Hoyle state, or the study of the behavior of the nuclear fluid at low-density [1]}, [2]}, [3]}, [4]}, [5]}, [6]}. For a decade, the nucleonic localization function (NLF) has increasingly been used to tag the formation of alpha-particles [7]}, [8]}, [9]}, [10]}, [11]}, [12]}, [13]}, such as in cluster states, or during the fission process. It is therefore important to understand its usefulness and limitations in details. Concomitantly, the use of Relativistic Mean Field (RMF) Energy Density Functional (EDF) approaches has been shown to pinpoint localized alpha structures in nuclei [14]}, [15]}, [16]}, [17]}, [18]}, [19]}, [20]}, [21]}, [22]}. This is less the case with Skyrme EDF approaches, where localized alpha-particle structures do not appear in the density, unless strong constraints are considered, such as in the case of high-spin rotations [23]} or very large deformations [7]}. This difference in behavior between the RMF and Skyrme densities was related to the difference in the depth of the mean-field potential [15]}.
